1. Field of the Invention
The present invention relates to the field of signal processing, and in particular, to signal processing in a partial-response (PR) read channel.
2. Background Art
Communication of voice and data signals is often accomplished by converting analog signals to digital signals. These digital signals are then transmitted from a transmitting device to a receiving device, converted back to analog, if necessary, and communicated to a user. This digital transmission is often performed through analog channels. Digital information is transmitted in the form of a "symbol" representing a digital value. In some cases, adjacent symbols can overlap, resulting in a phenomenon known as intersymbol interference. This interference can corrupt a digital transmission, leading to errors in the receipt of the digital information.
Using partial-response signaling allows a better handling of intersymbol interference and allows a more efficient utilization of the bandwidth of a given channel. In partial-response systems, a controlled amount of intersymbol interference can be allowed. The partial-response system is described by the polynomials 1+D, 1-D and (1-D.sup.2), also called duobinary, dicode, and class-IV, respectively.
Class IV partial-response waveforms are formed by the subtraction of binary waveforms two bit intervals apart. This process boosts midband frequencies making the system more immune to noise and distortion at both high and low frequencies. This is especially useful in a magnetic recording channel where, using a conventional inductive head, there is little signal at low frequencies and spacing losses can cause large attenuation at high frequencies.
Partial-response (PR) signaling allows a better handling of intersymbol interference and allows a more efficient utilization of the bandwidth of a given signal detection channel. A general description of partial-response signaling principles is given by P. Kabal and S. Paupathy in "Partial-Response Signaling", IEEE Transaction on Communications, Vol. COM-23, No. 9, September 1975, pp. 921-934.
Because class IV partial-response signaling for digital detection is especially suited for the magnetic recording channel, sampled amplitude detection can be applied for magnetic recording. To minimize the propagation of data errors, the signal is turned into a sequence of binary numbers. Procedures for determining the maximum likelihood sequence in the presence of noise can then be applied. With sequence detection, sequences of bits are detected and processed to minimize error.
With PR signaling, tasks such as maximum-likelihood sequence detection (MLSD) and sample time recovery have been described by G. D. Forney in "Maximum-Likelihood Sequence Estimation of Digital Sequences in the Presence of Intersymbol Interference", IEEE Transaction on Information Theory, Vol. IT-18, No. 3, May 1972, pp. 363-378, and by Mueller et al., "Timing Recovery in Digital Synchronous Data Receivers", IEEE Transactions on communications, Vol. COM-24, No. 5, May 1976, pp. 516-531.
Another task associated with PR signaling is equalizing the signal channel bandwidth response. Without proper shaping of the read signal, the signal samples will not be at their desired values, and errors will occur. An optimal channel is achieved by matching the unfiltered channel response to the desired PR response. Adaptive equalization of a magnetic recording PR channel is described in U.S. Pat. No. 5,060,088 granted to F. B. Dolivo, et al., and in R. D. Cideciyan, et al. "A PRML System for Digital Magnetic Recording", IEEE Journal on Selected Areas in Communications, Vol. 10, No. 1, January 1992, pp. 38-56.
In prior art systems, methods for equalization and tinning recovery utilize the error from samples that quantize to values other than zero. Because the equalizer adaptation algorithm employs multiplication of these non-zero values, the prior art systems are sensitive to both amplitude and timing errors. These errors manifest directly in the tap coefficients of the equalizer and result in a mismatch between the channel characteristics and the equalizer frequency response.
In any system with multiple self adapting feedback loops, it is extremely desirable to have the loops orthogonal or non-interacting to minimize "hunting" or jittering about the desired loop operation points. By using non-zero valued samples, the equalization, automatic gain control (AGC) and timing recovery loops are interdependent, e.g. an adaptation in the gain control circuit will affect the adaptation of the equalizer.
One suitable design for a PR channel equalizer is the adaptive cosine equalizer (ACE). An adaptive cosine equalizer with an input sampler is shown in FIG. 1. Sampled input signal 100 (x.sub.n) is provided to delay 101, and, as the first tap of the delay line, to multiplier 105. The output of delay 101 comprises second tap signal 102 (x.sub.n-1) and is coupled to delay 103 and summing means 110. The output of delay 103 comprises the third tap signal 104 (x.sub.n-2) that is provided to multiplier 107. Tap coefficient 106 (K) is provided to multipliers 105 and 107. Modified tap values 108 and 109, provided by multipliers 105 and 107, respectively, are coupled to summing means 110. Summing means 110 generates output signal 111 (y.sub.n).
The input signal is sampled at times (nT+.tau.), where `T` is the sampling period. The cosine equalizer is comprised of a delay line having two delay elements 101 anti 103 of value `T`, and three taps, 100, 102 and 104. The sample of the center tap 102, and the modified samples of the two outer taps 102 and 104, each of the outer taps weighted with tap coefficient `K` 106, are combined in summing means 110 to form output sample `Y.sub.n ` 111. The output sample `y.sub.n ` is given by: EQU y.sub.n =x.sub.n-1 +K(x.sub.n +x.sub.n-2)
Taking the Fourier transform, the equalizer frequency response is shown to be that of a linear phase filter with EQU .vertline.H(w).vertline.=.vertline.1+2Kcos(w).vertline.
where w=2.pi.fT and `f` is the sampling frequency. For values of K between zero and one-half, lower frequencies are boosted and higher frequencies are attenuated. For values of K between zero and negative one-half, the inverse is true. By varying K, the filter response can be tuned to counteract the effects of the unfiltered frequency response of the unfiltered channel. Ideally, where H'(w) is the frequency response of the unfiltered channel, EQU .vertline.H'(w)H(w).vertline.=.alpha.
where .alpha.=some chosen gain constant. This means that all actions of the channel on the signal are completely canceled by the actions of the equalizer, except for some possible phase contributions. An adaptive algorithm is used to update coefficient K such that the equalizer matches the channel as closely as possible.
FIG. 2 illustrates the adaptive cosine equalizer of Dolivo et al. Included in the drawing are apparatus for generating the sample-to-sample adjustments to the tap coefficient, .DELTA.K.sub.n, and apparatus for generating the tap coefficient, K.sub.n. Input signal 200 is coupled to delay 201, and provided as the first tap of the tapped delay line to summing means 207. Delay 201 provides signal 202 to delay 203, and also, as the second tap of the tapped delay line, to summing means 210. Delay 203 provides signal 204 as the third tap of the tapped delay line to summing means 207. Summing means 207 provides signal 208 to multiplier 205 and adaptive update means 213. Coefficient signal 206 is provided to multiplier 205. Multiplier 205 provides cosine term 209 to summing means 210. Summing means 210 generate output signal 211 that is provided to adaptive update means 213.
Within adaptive update means 213, quantization means 212 and 214 receive input signals 208 and 211, respectively. Subtraction means 215 also receive signal 211 on a positive input port. Quantization means 214 provide signal 236 to a negative input port of subtraction means 215. Subtraction means 215 provide error signal 216 to multiplier 218. Quantization means 212 provide signal 217 to multiplier 218. Output signal 219 of multiplier 218 is coupled to delay 220 and summing means 222. Delay 220 provides delay signal 221 to summing means 222. Summing means 222 generates incremental update signal 223, the stochastic gradient, that is provided to tap coefficient adjustment means 235.
Within tap coefficient adjustment means 235, incremental update signal 223 is provided to multiplier 224. High sample value 227 and low sample value 228 are provided to selector 226. Selector 226 provides signal 229 to multiplier 224. Multiplier 224 is coupled to loop delay 230 via signal 225. Loop delay 230 provides delayed signal 231 to a negative input port of subtraction means 232. Loop delay 230 models the latency of the coefficient update circuit. Subtraction means 232 provide coefficient signal 206 to delay 233 and multiplier 205 of the cosine filter. Delay 233 provides delayed signal 234 to a positive input port of subtraction means 232.
The updating algorithm of Dolivo et al. generates the stochastic gradient,.DELTA.K.sub.n. The stochastic gradient is given by, EQU .DELTA.K.sub.n =e.sub.n u.sub.n +e.sub.n-1 u.sub.n-1
where EQU e.sub.n =y.sub.n -z.sub.n EQU u.sub.n =x.sub.n +x.sub.n-2
u.sub.n is the quantized value of u.sub.n at sampling instant n. z.sub.n is the ideal quantized output of y.sub.n. The quantization is performed such that ##EQU1##
The circuit of FIG. 2 performs the operations above in the following manner. A tapped delay line comprising delays 201 and 203 generates signals x.sub.n, x.sub.n-1 and x.sub.n-2. x.sub.n and x.sub.n-2 are summed (means 207) to generate u.sub.n that is then quantized (means 212) into u.sub.n. u.sub.n is multiplied (means 205) by the coefficient K.sub.n to generate the cosine term that is summed (means 210) with X.sub.n-1 to generate Y.sub.n.
y.sub.n is quantized (means 214) into z.sub.n, and then the difference (means 215) between y.sub.n and z.sub.n is taken as the error e.sub.n. u.sub.n and e.sub.n are multiplied (means 218) to generate the term u.sub.n e.sub.n, which is delayed (means 220) to generate u.sub.n-1 e.sub.n-1. The stochastic gradient, .DELTA.K.sub.n, is generated by summing (means 222) these two terms together.
The coefficient K.sub.n is generated by subtracting (means 232) .DELTA.K.sub.n from the previous coefficient K.sub.n-1. This is equivalent to multiplying .DELTA.K.sub.n by negative one and supplying that to an integrator (means 232 and 233). To account for bandwidth limitations in the integrator hardware, a pre-scaling operation (means 224, 226, 227 and 228) is performed on .DELTA.K.sub.n.
The circuit of FIG.2 is susceptible to misequalization due to gain control errors. Assuming a gain error factor .beta., EQU y.sub.n (.beta.x.sub.n)=.beta.x.sub.n-1 +K(.beta.x.sub.n +.beta.x.sub.n-2)=.beta.[x.sub.n-1 +K(x.sub.n +x.sub.n-2)]=.beta.y.sub.n (x.sub.n)
Thus, gain errors propagate proportionally from input to output of the equalizer. The incremental error seen by the adaptation circuit is: EQU .DELTA.K'.sub.n,error .infin..beta.y.sub.n -z.sub.n -(y.sub.n -z.sub.n)=y.sub.n (.beta.-1)
The error is proportional to y.sub.n. Therefore, larger values of yn are more sensitive to gain error. The updating algorithm will attempt to offset the low frequency gain error by adapting the low frequency characteristics of the cosine equalizer. This will cause the high frequency response of the equalizer to rise or fall erroneously. A less sensitive scheme is desired.
In addition to gain error sensitivity, the circuit of FIG. 2 is susceptible to timing errors. FIGS. 3A and 3B show the effect of timing errors on an isolated PR4 pulse and a dibit PR4 pulse, respectively. The "o" indicates the ideal sample point value and "x" indicates the phase-shifted sample point value. The errors e.sub.1, e.sub.2, e.sub.3, etc. are the error signal caused by a sample timing error. For the isolated pulse of FIG. 3A, taking into account the direction of the errors, the summation of .DELTA.K.sub.n of the sample errors is EQU .SIGMA..DELTA.K.sub.n =-e.sub.2 +e.sub.3 -e.sub.2 +e.sub.4 +e.sub.3 -e.sub.5 +e.sub.4 -e.sub.5 =2(-e.sub.2 +e.sub.3 +e.sub.4 -e.sub.5)
It can be seen that, assuming relatively similar error magnitudes, error terms tend to cancel. However, for the dibit pulse of FIG. 3B, the summation of .DELTA.K.sub.n is EQU .SIGMA..DELTA.K.sub.n =-2e.sub.2 -2e.sub.6 =-2(e.sub.2 +e.sub.6)
For the dibit pulse, the errors don't cancel. The residual error can result in misequalization as it builds in the adaptation integrator over time. Because the circuit of FIG. 2 is sensitive to gain and timing errors, adaptation of timing and gain loops will cause errors in the adaptation of the equalizer as the loops interact.